Electrical Machine-I (EX-402) Unit 1 Notes

UNIT 1: ELECTRICAL MACHINES - TRANSFORMERS & INDUCTION MOTORS

I. TRANSFORMERS (Core & Advanced Concepts)

1.1 Constructional Features & Basic Principle

Core Type: Windings surround the core limbs. Easier to manufacture, better cooling for large units.
Shell Type: Core surrounds the windings. More mechanically robust, shorter magnetic path.
Core Materials: High-grade silicon steel (reduces hysteresis & eddy losses). Laminated (0.35-0.5 mm thick) to minimize eddy currents. Insulation between laminations (e.g., varnish).
Windings: Primary (input), Secondary (output), Tertiary (for auxiliary loads or harmonic suppression). Materials: Copper (high conductivity) or Aluminum (lighter, cheaper). Insulation classes (A, B, F, H) define maximum operating temperature.
Main Parts: Tank (holds core & windings, filled with oil), Bushings (insulated terminals), Conservator (accommodates oil expansion), Breather (drying agent like silica gel).

Principle: Mutual induction. AC supply to primary creates alternating flux in core, linking secondary to induce EMF.

1.2 Fundamental Equations & Operation

EMF Equation (per phase):

$$E = 4.44 f N \phi_m$$

Where $f$ = frequency, $N$ = number of turns, $$\displaystyle \phi_m $$ = maximum flux in core.

Turns Ratio & Voltage Transformation Ratio:

$$a = \frac{N_1}{N_2} = \frac{V_1}{V_2} \text{ (Ideal)}$$

$$\frac{V_1}{V_2} \approx \frac{E_1}{E_2} = \frac{N_1}{N_2} \text{ (Practical)}$$

Ideal Transformer: No losses, no leakage flux, 100% efficiency. $$\displaystyle V_1 I_1 = V_2 I_2 $$.
Practical Transformer: Has core losses (no-load) and copper losses (on-load).
No-Load Operation:
- Primary draws no-load current $$\displaystyle I_0 $$.
- $$\displaystyle I_0 = I_w + I_m $$ (Phasor sum).
  - $$\displaystyle I_w $$ (Active/Core loss component): In phase with $$\displaystyle V_1 $$, supplies hysteresis & eddy losses.
  - $$\displaystyle I_m $$ (Magnetizing component): Lags $$\displaystyle V_1 $$ by 90°, produces mutual flux $$\displaystyle \phi_m $$.
- No-load power factor is low ($$\displaystyle \cos \phi_0 \approx 0.2-0.4 $$).
On-Load Operation: Secondary current $$\displaystyle I_2 $$ creates MMF $$\displaystyle N_2 I_2 $$ which demagnetizes core. Primary draws load current $$\displaystyle I_1 $$ to maintain net MMF ($$\displaystyle N_1 I_1 - N_2 I_2 = N_1 I_0 $$).

1.3 Performance Characteristics & Tests

Open Circuit (OC) Test

Purpose: Determine core loss parameters ($$\displaystyle R_0 $$, $$\displaystyle X_m $$) and core loss at rated voltage.
Procedure: LV side energized, HV side open. Apply rated voltage $$\displaystyle V_1 $$.
Measurements: $$\displaystyle V_1 $$, $$\displaystyle I_0 $$, $$\displaystyle P_0 $$ (Wattmeter reading = core loss $$\displaystyle P_i $$).
Calculations:

$$P_0 = P_i = \text{Hysteresis} + \text{Eddy loss}$$

$$I_w = \frac{P_0}{V_1}, \quad I_m = \sqrt{I_0^2 - I_w^2}$$

$$R_0 = \frac{V_1}{I_w}, \quad X_m = \frac{V_1}{I_m}$$

Short Circuit (SC) Test

Purpose: Determine equivalent resistance ($$\displaystyle R_{eq} $$) and reactance ($$\displaystyle X_{eq} $$) for voltage regulation, and full-load copper loss.
Procedure: HV side energized (low voltage), LV side shorted. Apply voltage $$\displaystyle V_{sc} $$ to draw rated current $$\displaystyle I_{1(rated)} $$.
Measurements: $$\displaystyle V_{sc} $$, $$\displaystyle I_{1(rated)} $$, $$\displaystyle P_{sc} $$ (Wattmeter reading = full-load copper loss $$\displaystyle P_{c(FL)} $$).
Calculations:

$$P_{sc} = I_{1(rated)}^2 R_{eq} \Rightarrow R_{eq} = \frac{P_{sc}}{I_{1(rated)}^2}$$

$$Z_{eq} = \frac{V_{sc}}{I_{1(rated)}}, \quad X_{eq} = \sqrt{Z_{eq}^2 - R_{eq}^2}$$

*   $$\displaystyle R_{eq} = R_1 + R_2' $$, $$\displaystyle X_{eq} = X_1 + X_2' $$ (referred to primary).

Sumpner's Test (Back-to-Back Test)

Purpose: Predetermine efficiency and regulation under loaded conditions simultaneously.
Procedure: Two identical transformers connected back-to-back (LV of T1 to LV of T2). Primary of T1 fed from supply, secondary of T2 shorted. Adjust T2's secondary voltage to oppose T1's secondary voltage. Total input power to T1 = Core loss of both + Copper loss of both.
Advantage: Simulates actual loading without needing large load.

Losses

Core (Iron) Losses: Constant (independent of load).
- Hysteresis Loss: $$\displaystyle P_h \propto f B_m^n $$ (Steinmetz eqn: $$\displaystyle P_h = \eta B_m^n f $$), $n \approx 1.6-2.0$.
- Eddy Current Loss: $$\displaystyle P_e \propto f^2 B_m^2 t^2 $$ (t = lamination thickness).
Copper Losses: Vary with load squared ($$\displaystyle P_c \propto I^2 $$).
Stray Losses: Due to leakage flux causing eddy currents in structural parts (~0.5-1% of total loss).

Efficiency

Definition: $$\displaystyle \eta = \frac{\text{Output Power}}{\text{Input Power}} = \frac{P_o}{P_o + P_i + P_c} $$
Condition for Maximum Efficiency: $$\displaystyle \frac{d\eta}{dP_o} = 0 \Rightarrow P_c = P_i $$.
- Occurs at load $$\displaystyle x = \sqrt{\frac{P_i}{P_{c(FL)}}} $$ (fraction of full load).
- $$\displaystyle \eta_{max} = \frac{x \cdot S \cdot \cos\phi}{x \cdot S \cdot \cos\phi + P_i + x^2 P_{c(FL)}} $$ at $$\displaystyle x = \sqrt{P_i/P_{c(FL)}} $$.
All-Day Efficiency: $$\displaystyle \eta_{ad} = \frac{\text{Energy output (24h)}}{\text{Energy input (24h)}} $$. Important for distribution transformers with varying load.

Voltage Regulation

Definition: Change in secondary terminal voltage from no-load to full-load, at constant primary voltage & same power factor, expressed as % of rated secondary voltage.

$$\%VR = \frac{V_{2(NL)} - V_{2(FL)}}{V_{2(FL)}} \times 100\%$$

Exact Formula:

$$VR = \frac{I_2 R_{02} \cos\phi_2 \pm I_2 X_{02} \sin\phi_2}{V_2} \times 100\%$$

(+ for lagging PF, - for leading PF).

Approximate Formula (primary referred):

$$VR \approx \frac{I_1 R_{eq} \cos\phi \pm I_1 X_{eq} \sin\phi}{V_1} \times 100\%$$

Condition for Zero Regulation: Leading PF such that $$\displaystyle I R \cos\phi = I X \sin\phi \Rightarrow \tan\phi = \frac{R}{X} $$.
Condition for Maximum Regulation: Lagging PF such that $$\displaystyle \sin\phi = 1 $$ (0.1 PF lagging).

Phasor Diagrams: Draw for lagging, unity, and leading power factors to visualize voltage drop components.

1.4 Advanced Transformer Topics

Auto-transformer

Construction: Single continuous winding with a tap. Common section (AB) and series section (BC).
Principle: Both primary and secondary share part of the winding. Voltage transformation via self-induction & mutual induction.
Comparison with Two-Winding Transformer:

| Feature | Two-Winding Transformer | Auto-transformer | | :--- | :--- | :--- | | Winding | Two separate, electrically isolated | One continuous winding | | Size/Weight | Larger, heavier | Smaller, lighter (for same rating) | | Efficiency | Slightly lower | Higher (less copper & core) | | Voltage Regulation | Poorer | Better | | Short Circuit Current | Lower | Higher (impedance lower) | | Application | Isolation needed, large ratio changes | Voltage regulation, motor starting, interconnecting systems |
Saving in Copper: For transformation ratio $$\displaystyle a = V_1/V_2 $$ (assume $$\displaystyle a>1 $$), mass of copper in auto-transformer $\propto (1 - 1/a)$ times that of two-winding transformer.
Applications: Voltage regulators, starter for induction motors, interconnection transformers (e.g., 132kV/220kV).

Parallel Operation

Conditions for Successful Parallel Operation:
1. Same Voltage Ratio: $$\displaystyle |V_1|/|V_2| $$ must be equal. Prevents circulating currents.
2. Same % Impedance: $$\displaystyle Z_{eq1}\% = Z_{eq2}\% $$. Ensures kVA sharing proportional to ratings.
3. Same Polarity: Correct phase sequence & polarity. Prevents short-circuit.
4. Same Phase Sequence: For three-phase transformers.
Load Sharing: With equal voltage ratios & impedances, load shared proportional to kVA ratings.

$$\frac{S_1}{S_{1(rated)}} = \frac{S_2}{S_{2(rated)}} \text{ if } Z_1\% = Z_2\%$$

Circulating Currents: Arise from unequal voltage ratios or unequal % impedances. Cause extra losses & reduce capacity.

Three-Phase Transformers

Connections:

| Primary | Secondary | Application | | :--- | :--- | :--- | | Y-Y | Y-Y | Rare (neutral instability, 3rd harmonics) | | Δ-Δ | Δ-Δ | Balanced loads, no neutral | | Y-Δ | Y-Δ | Step-down, LV side neutral available | | Δ-Y | Δ-Y | Step-up, HV side neutral available | | Zig-Zag | - | Neutral grounding, harmonic suppression |
Scott Connection: Two single-phase transformers (Main $$\displaystyle T_m $$ & Teaser $$\displaystyle T_t $$) to convert 3-phase to 2-phase or vice-versa.
- Main Transformer: Center-tapped on primary (connected to line A & C of 3-phase). Secondary gives 90° phase shift.
- Teaser Transformer: Primary connected between line B and center-tap of main primary (ratio $\sqrt{3}/2$ times main). Secondary in series with main secondary.
- Proof: With balanced 3-phase supply $$\displaystyle V_{AN} $$, $$\displaystyle V_{BN} $$, $$\displaystyle V_{CN} $$, phasor diagram shows secondary voltages $$\displaystyle V_{2m} $$ and $$\displaystyle V_{2t} $$ are equal in magnitude and 90° apart (2-phase).
- Applications: Supplies 2-phase electric arc furnaces, 2-phase traction systems.

Special Transformers

Cooling Methods:
- ONAN: Oil Natural, Air Natural (small units).
- ONAF: Oil Natural, Air Forced (fans).
- OFAF: Oil Forced, Air Forced (pumps + fans, large units).
- OFWF: Oil Forced, Water Forced (very large, water-cooled heat exchangers).
Conservator & Breather:
- Conservator: Sealed drum above main tank. Allows oil expansion/contraction with temperature, prevents air contact with oil in main tank.
- Breather: Contains silica gel (blue when dry, pink when moist). Connected between conservator & atmosphere. Absorbs moisture from air entering conservator, prevents oil deterioration.
- Necessity: Moisture reduces insulation strength, oxygen causes oxidation & sludge formation.
Tap Changer:
- Off-Circuit (OCTC): Operates when transformer is de-energized. For infrequent voltage adjustments.
- On-Load Tap Changer (OLTC): Operates under load. Complex (selector + diverter switches). Used for voltage regulation in power systems.
- Necessity: Compensate for system voltage variations, maintain secondary voltage constant.
Pulse & High-Frequency Transformers:
- Core: Ferrite or powdered iron (low loss at high freq).
- Construction: Minimize inter-winding capacitance, leakage inductance. Often toroidal or planar.
- Applications: Pulse transformers (digital circuits, gate drives), HF transformers (switch-mode power supplies, inverters).
Power vs. Distribution Transformers:

| Feature | Power Transformer | Distribution Transformer | | :--- | :--- | :--- | | Rating | > 200 MVA (usually) | < 200 MVA (typically 25-2500 kVA) | | Voltage | Very high (EHV/UHV) | Medium/Low (33kV/11kV to 415V) | | Application | Substations, transmission | End-user, pole-mounted, pad-mounted | | Efficiency | > 99.5% (max. efficiency at full load) | 98-99% (max. efficiency at ~50-70% load) | | Design Focus | Low impedance for fault current, high efficiency at full load | Low no-load loss, good regulation at light loads |

Inrush Current

Nature: Large, asymmetric DC offset decaying sinusoid. Can be 8-30 times rated current.
Causes: Transformer core flux $$\displaystyle \phi = \int v dt $$. At energization, if core has residual flux $$\displaystyle \phi_r $$, applied voltage may drive flux to $$\displaystyle \phi_{max} + \phi_r $$ (twice normal), requiring large magnetizing current.
Problems: Maloperation of protection relays (differential, overcurrent), mechanical stress on windings, voltage dip in supply system.

Effect of Harmonics

Core Loss: Increases (hysteresis loss $\propto f$, eddy loss $$\displaystyle \propto f^2 $$).
Heating: Additional eddy currents in tank, structural parts (stray losses).
Neutral Current: In Y-connected secondary with unbalanced non-linear loads, triplen (3rd, 9th...) harmonics add in neutral, causing overheating.
Torque Pulsations: In motors supplied via transformer, harmonic voltages cause torque ripple.

Negative Sequence Current

Effect on Transformers: Creates reverse rotating field in core. Causes additional eddy current losses in structural parts (tank, clamping plates) → localized heating. Does not produce net flux in core (counter-rotating fields cancel), so no useful output. Reduces capacity.

II. THREE-PHASE INDUCTION MOTOR (Core & Analysis)

2.1 Construction & Working Principle

Stator: laminated core, 3-phase distributed winding in slots. Produces rotating magnetic field (RMF) at synchronous speed $$\displaystyle N_s = \frac{120f}{P} $$.
Rotor:
- Squirrel Cage: Al/Cu bars short-circuited by end rings. Simple, rugged, cheap.
- Slip Ring (Wound Rotor): 3-phase star-connected winding, 3 slip rings, brushes. Allows external resistance insertion.
Slip (s): $$\displaystyle s = \frac{N_s - N_r}{N_s} $$. Measures relative speed. Rotor EMF $$\displaystyle E_2 = s E_{20} $$ (standstill). Rotor frequency $$\displaystyle f_2 = s f $$.

2.2 Equivalent Circuit & Performance Equations

Approximate Equivalent Circuit (Referred to Stator):
```
V1 --[R1 + jX1]--[Rm // jXm]--[R2'/s + jX2']-- 0
```
Where $$\displaystyle R_2' = R_2 \cdot a^2 $$, $$\displaystyle X_2' = X_2 \cdot a^2 $$, $$\displaystyle a = \frac{N_1}{N_2} $$ (turns ratio).
Torque-Slip Equation (Derived from power flow):

$$T = \frac{3}{\omega_s} \cdot \frac{s E_2^2 R_2}{R_2^2 + (s X_2)^2}$$

Where $$\displaystyle \omega_s = \frac{2\pi N_s}{60} $$ (synchronous rad/s), $$\displaystyle E_2 $$ = standstill rotor EMF.

\boxed{T = \frac{k s E_2^2 R_2}{R_2^2 + (s X_2)^2}} \quad (k = \frac{3}{\omega_s})

Slip at Maximum Torque:

Differentiate T w.r.t s, set dT/ds=0.

\boxed{s_m = \frac{R_2}{X_2}}
Maximum Torque:

Substitute $$\displaystyle s_m $$ in T equation.

\boxed{T_{max} = \frac{k E_2^2}{2 X_2}} \quad (Independent of $$\displaystyle R_2 $$)
Power Flow in Rotor:
- Rotor Input (Air-gap power $$\displaystyle P_2 $$): Power transferred across air-gap.
- Rotor Copper Loss ($$\displaystyle P_{cu2} $$): $$\displaystyle P_{cu2} = s P_2 $$.
- Mechanical Output ($$\displaystyle P_m $$): $$\displaystyle P_m = P_2 - P_{cu2} = (1-s) P_2 $$.
\boxed{P_m = (1-s) P_2}, \quad \boxed{P_{cu2} = s P_2}

2.3 Characteristics & Analysis

Torque-Speed Characteristic:
- Region 0 < s < 1 (Motoring): T positive, N_r positive. Stable operating region (slope negative).
- s = 0 (Synchronous speed): T = 0.
- s = 1 (Start/Blocked rotor): Starting torque $$\displaystyle T_{st} = \frac{k E_2^2 R_2}{R_2^2 + X_2^2} $$.
- s = s_m: Maximum torque $$\displaystyle T_{max} $$.
- Effect of Rotor Resistance: Increasing $$\displaystyle R_2 $$ shifts $$\displaystyle s_m $$ right (higher starting torque, lower starting current), $$\displaystyle T_{max} $$ unchanged.
- Squirrel Cage: Low $$\displaystyle R_2/X_2 $$ → low $$\displaystyle s_m $$ (0.02-0.05), high efficiency, low starting torque.
- Slip Ring: High $$\displaystyle R_2 $$ possible → high $$\displaystyle s_m $$, high starting torque.
Crawling & Cogging:
- Crawling: Motor runs at ~1/7th of synchronous speed due to space harmonics (especially 7th harmonic → negative sequence field rotating opposite). Prevent by proper stator winding design (chording), avoiding slot harmonics.
- Cogging (Locking): Motor fails to start. Rotor tends to lock in position with stator slots due to slot harmonics (magnetic attraction between stator & rotor slots). Prevent by using fractional slot winding, skewing rotor bars.
Circle Diagram:
- Construction: From no-load test (gives $$\displaystyle I_0 $$, $$\displaystyle P_0 $$) and blocked-rotor test (gives $$\displaystyle I_{sc} $$, $$\displaystyle P_{sc} $$, $$\displaystyle V_{sc} $$). Plot on complex plane (stator current vs. power input).
- Parameters from Diagram:
  - Full-load current & PF: Locate point at rated power (P) along power line.
  - Maximum torque & slip: Tangent from origin to circle.
  - Starting torque: Intersection of circle with $$\displaystyle P=0 $$ line.
  - Efficiency & PF at any load: Read corresponding P and I.
Losses & Efficiency:
- Stator Copper Loss: $$\displaystyle 3 I_1^2 R_1 $$.
- Stator Core Loss: $$\displaystyle P_i $$ (from OC test, assumed constant).
- Rotor Copper Loss: $$\displaystyle s \cdot P_2 $$ (air-gap power).
- Friction & Windage Loss: $$\displaystyle P_{fw} $$ (mechanical losses, constant at constant speed).
- Efficiency: $$\displaystyle \eta = \frac{P_m}{P_{in}} = \frac{P_m}{P_m + \text{all losses}} $$.

2.4 Starting Methods

Direct-on-Line (DOL): Full voltage applied. High starting current (5-8×FL), moderate starting torque. Used for small motors (< 5-10 HP).
Star-Delta (Y-Δ) Starter: Stator winding starts in star (voltage/√3, current/3), switches to delta. Reduces starting current & torque to 1/3. Used for delta-connected motors > 5 HP.
Auto-transformer Starter: Reduced voltage via autotransformer taps (50%, 65%, 80%). Reduces starting current & torque proportional to voltage².
Rotor Resistance Starter (Slip Ring IM): External resistances in rotor circuit. High starting torque, low starting current, smooth acceleration. Resistors cut out in steps as motor speeds up.
Double Cage & Deep Bar Rotor:
- Construction: Two parallel rotor circuits (outer cage: high resistance, low leakage reactance; inner cage: low resistance, high leakage reactance).
- Principle: At start (high slip, high $$\displaystyle f_2 $$), skin effect increases impedance of inner cage → current flows mainly in outer cage (high $R$) → high starting torque, low starting current. At run (low slip, low $$\displaystyle f_2 $$), skin effect negligible → both cages conduct (low net $R$) → good efficiency.
- Torque-Slip: Higher starting torque than single cage, similar $$\displaystyle T_{max} $$.

2.5 Speed Control Methods

From Stator Side:
1. V/f Control: Vary voltage & frequency proportionally to maintain constant air-gap flux. Wide speed range. Used in VFDs.
2. Pole Changing: Change number of poles (P) by altering stator winding connections. Step change in speed ($$\displaystyle N_s \propto 1/P $$). Used in multi-speed motors.
3. Voltage Control: Reducing voltage reduces torque (T ∝ V²). Used for small speed variations in fan/pump loads (inefficient).
From Rotor Side (Slip Ring IM only):
1. Inserting Rotor Resistance: Increases slip for given load → reduces speed. Torque remains same. Simple but inefficient (resistance losses).
2. Cascade Connection: Two motors on same shaft. Rotor of main motor (slip ring) fed to stator of auxiliary motor. Gives two fixed speeds.

2.6 Effects of Supply Variations

Voltage Variation:
- Torque $$\displaystyle T \propto V^2 $$. 10% voltage drop → ~19% torque drop.
- Slip increases to maintain load torque → rotor current ↑, efficiency ↓.
- Magnetizing current ↓ slightly.
Frequency Variation:
- Synchronous speed $$\displaystyle N_s \propto f $$. 10% frequency increase → 10% speed increase.
- If voltage constant, flux $\phi \propto V/f$ ↑ → core saturation, magnetizing current ↑, core loss ↑, noise ↑.
- If V/f kept constant (VFD), flux constant → normal operation.
Unbalanced Supply / Negative Sequence Currents:
- Negative sequence voltage produces reverse rotating field.
- Causes: Additional copper losses (stator & rotor), heating (especially rotor bars/end rings), reduced torque, vibration, noise.
- Effect: Motor may overheat at lower loads than rated.

III. SINGLE-PHASE & SPECIAL MOTORS

3.1 Single-Phase Induction Motor

Why Not Self-Starting? Single-phase supply produces pulsating (not rotating) magnetic field. At start, net torque zero (double revolving field theory: two equal & opposite fields → equal & opposite torques).
Double Revolving Field Theory: Pulsating field resolved into two rotating fields ($$\displaystyle F_f $$, $$\displaystyle F_b $$) of equal magnitude, rotating in opposite directions at $$\displaystyle N_s $$. Each induces rotor EMF/current. Starting torque $$\displaystyle T_{st} = T_f - T_b = 0 $$.
Starting Mechanisms: Provide auxiliary starting winding with phase shift (capacitor or resistance) to create asymmetry → unbalanced fields → net starting torque.
Types & Starting Mechanisms:
- Split-Phase (Resistance Start): Main winding (high inductance), Auxiliary winding (high resistance). High R/X ratio in aux → phase shift ~25°. Moderate starting torque.
- Capacitor Start: Capacitor in series with aux winding → large phase shift (~80°). High starting torque. Capacitor disconnected by centrifugal switch.
- Capacitor Start-Capacitor Run: Two capacitors (start & run). High starting torque & good running PF. Expensive.
- Shaded-Pole: Shading ring (copper) on part of pole. Induced current in ring lags flux → weak rotating field. Low starting torque, cheap. Used in small fans, clocks.

3.2 Single-Phase AC Series Motor (Universal Motor)

Construction: Similar to DC series motor. Compensating winding (embedded in pole faces) & interpole (commutation pole) to improve commutation.
Working Principle: AC supply → alternating flux → alternating torque. Series connection → field & armature currents always in phase → unidirectional torque. Commutation poor due to alternating flux → hence compensating winding.
Characteristics: Very high speed (up to 20,000 rpm), high starting torque, light weight. Speed varies inversely with load.
Applications: Portable tools (drills, saws), vacuum cleaners, domestic appliances.
Role of Compensating Winding: Produces local flux opposing armature MMF, reduces reactance voltage, improves commutation, reduces sparking.

3.3 AC Servo Motor

Construction: 2-phase or 3-phase induction motor with cage rotor (low inertia). Two stator windings spaced 90° electrical: Control winding (voltage controlled), Reference/Auxiliary winding (constant voltage, often with capacitor for 90° phase shift).
Working Principle: Control voltage $$\displaystyle V_c $$ applied to control winding. Rotor rotates to align with resultant RMF. Torque proportional to $$\displaystyle V_c $$ and sine of torque angle $\delta$ ($$\displaystyle T \propto V_c \sin\delta $$). Small control voltage → precise speed/position control.
Applications: Speed control in machine tools, position control in radar antennas, robotics, automatic control systems.

3.4 Linear Induction Motor (LIM)

Principle: "Unwrapped" rotary induction motor. Stator (primary) laid flat, rotor (secondary) as flat plate or tubular. Travelling magnetic field induces linear motion.
Construction Types:
- Flat Primary: Short primary on one side of reaction plate (Al/ Cu sheet on iron). Used in maglev, conveyors.
- Tubular Secondary: Primary inside, secondary as moving tube (piston). Used in pumps, actuators.
Working: Synchronous speed $$\displaystyle v_s = 2f \tau $$ (τ = pole pitch). Slip $$\displaystyle s = \frac{v_s - v}{v_s} $$. Thrust $F \propto s$ (like torque ∝ s).
Applications: Maglev trains, baggage handling, sliding doors, liquid metal pumps, military launchers.

IV. COMPARATIVE & APPLICATION-BASED TOPICS

4.1 Transformer Comparisons

Auto-transformer vs. Two-winding: See Section 1.4 (Auto-transformer table).
Power vs. Distribution Transformer: See Section 1.4 (Power vs. Distribution table).

4.2 Induction Motor Comparisons

Squirrel Cage vs. Slip Ring Induction Motor:

| Feature | Squirrel Cage | Slip Ring (Wound Rotor) | | :--- | :--- | :--- | | Construction | Simple cage bars & end rings | 3-phase winding, slip rings, brushes | | Cost | Low | High | | Maintenance | Low (no brushes) | High (brushes, slip rings) | | Starting Torque | Low (1.5-2×FL) | High (2-3×FL) with external resistance | | Starting Current | High (5-8×FL) | Low (with rotor resistance) | | Speed Control | Difficult (V/f only) | Easy (rotor resistance) | | Efficiency | High | Slightly lower (rotor losses) | | Applications | Fans, pumps, compressors | Cranes, mills, elevators (high starting torque) |
Double Cage vs. Deep Bar Rotor:
- Both improve starting performance without external resistors.
- Double Cage: Two distinct cages with different R/X. Clear separation in torque-slip curve (two distinct peaks possible).
- Deep Bar: Single deep bar (skin effect increases effective R at start). Smoother torque-slip curve. Simpler construction.

4.3 Motor-Specific Topics

Starting Performance Improvement:
- Double Cage/Deep Bar: High starting torque, low starting current inherent.
- Wound Rotor + External Resistance: High starting torque, low current, smooth acceleration.
- Soft Starters/VFDs: Reduce voltage at start.
Braking Methods:
- Plugging (Reverse Current): Reverse supply polarity/sequence. Torque opposes rotation → rapid stop. High energy loss in rotor.
- Regenerative Braking: Motor speed > synchronous speed (e.g., downhill). Acts as generator, feed power back to supply. Requires VFD or special arrangement.
- Dynamic (Rheostatic) Braking: Disconnect AC, connect DC to stator → stationary field → generator action → energy dissipated in rotor resistance.
Steady-State Performance under Supply Variations: See Section 2.6.

4.4 Component/System Focus

Tap Changer: See Section 1.4 (Tap Changer).
Conservator & Breather: See Section 1.4 (Conservator & Breather).
Impact of Harmonics on IM:
- Torque Pulsations: Harmonic voltages produce rotating fields at harmonic speeds → torque ripple → vibration, noise.
- Heating: Additional eddy current & hysteresis losses in core & rotor (especially 5th, 7th harmonics).
- Efficiency Reduction: Increased losses.
- Neutral Current: In delta-connected stator, harmonic currents circulate in delta → extra heating. In star with neutral, triplen harmonics flow in neutral.

EXAM TIPS & COMMON PITFALLS

[!TIP] Transformer Regulation: Remember sign convention. Leading PF can give negative regulation. Zero regulation condition $$\displaystyle \tan\phi = R/X $$ is crucial.

[!TIP] Induction Motor Torque: $$\displaystyle T \propto s E_2^2 R_2 / (R_2^2 + (sX_2)^2) $$. Max torque independent of $$\displaystyle R_2 $$, but slip at max torque $$\displaystyle s_m = R_2/X_2 $$ depends on $$\displaystyle R_2 $$.

[!TIP] Circle Diagram: Always draw from OC & SC test data. The line from origin to point of maximum power is line of power factor (cos of angle with horizontal = PF at that load).

[!TIP] Scott Connection: Remember the 1:√3 ratio between main & teaser transformer kVA ratings. Teaser transformer kVA = $$\displaystyle \frac{\sqrt{3}}{2} $$ × main transformer kVA.

[!TIP] Double Cage vs. Deep Bar: Double cage has two distinct resistances; deep bar uses skin effect for frequency-dependent resistance.

[!TIP] Single-Phase IM Starting: Always explain using double revolving field theory. Starting torque zero because two opposite fields produce equal & opposite torques.

[!TIP] Auto-transformer Savings: Copper saving factor = $(1 - 1/a)$. For $$\displaystyle a=2 $$, saving = 50%. But isolation is lost.

[!TIP] Sumpner's Test: It's essentially two transformers connected back-to-back. Total input power = 2×Core loss + 2×Copper loss (at that load). Efficiency & regulation can be calculated directly.

[!TIP] Harmonics in Transformers: Remember triplen harmonics (3rd, 9th) are additive in neutral of Y-Y connection. Delta connection blocks them (circulate in delta).

[!TIP] Induction Generator: Needs reactive power supply (from grid or capacitors). Speed > synchronous speed ($$\displaystyle s < 0 $$). Slip negative → power flow reversed.

Account

Electrical Machine-I (EX-402) - Unit 1 Short Notes